JD 2018
Department of Mechanical Engineering
FACULTY OF ENGINEERING AND DESIGN
ME10010 Solid Mechanics 2 – Belt Drive Laboratory Exercise
Objectives
To investigate the relationship between tensions in a slipping pulley and compare this with results predicted by
theory.
Introduction
Belt drives are low cost, low maintenance devices used for the transmission of power from one machine to another.
The belt may be of rubber but synthetic materials and composite steel belts are commonly employed. Early belts
were flat and often made of leather but V and multi-groove V belts are now used since they transmit more power
for a given size pulley. The belt drive has a wide range of applications ranging from a food mixer or washing
machine with a power of a few 100 Watts to cars producing many kW's of power.
Gear based transmissions, although widely used, can only provide a limited number of gear ratios. The V belt has
the advantage that it can work on a pulley of variable diameter thus providing a relatively inexpensive form of
continuously variable transmission. The principal disadvantages of belt drives are the limited efficiency and slip
between the belt and the pulley which will influence the output speed and effective transmission ratio. The amount
of slip will depend upon the coefficient of friction between the belt and pulley, the belt profile and the torque
transmitted.
Theory
The relationship between tensions in a slipping pulley is examined in
detail by Grosjean [1] and Fawcett and Burdess [2]. It is shown that for
a stationary belt such as that shown in figure1, the ratio of tensions is as
follows
𝑇2
𝑇1= 𝑒(𝜇𝛽
𝑆𝑖𝑛𝛼)
where: T1........lower tension
T2....... higher tension
.........half V belt included angle (Figure 2)
.........angle of contact between belt and pulley (rad)
.........coefficient of friction
for a flat belt or string the angle is 90°.
The torque transmitted by a belt is given by
Torque = ( T2 - T1 ) R where R is the pulley radius (50mm)
The Power transmitted by a belt drive is given by the following equation
Power = Torque x where is the rotational speed in rads-1
Figure 1 Belt Drive Apparatus
T1
T2
1
R
Load
cell
Mg
2
Figure 2 V belt angle
JD 2018
Experimental Procedure
Apparatus
The experimental rig comprises of a variable speed DC electric motor driving a fixed radius pulley. A flat belt,
wrapped around the flat pulley, supports a series of masses on one end and a load cell on the other end. The
angle of contact between the belt and pulley can be set at four different values whilst the masses can be varied
from zero to 1 kg. The motor voltage and current is measured by digital meters whilst the pulley rotational speed
can be measured with a hand held optical tachometer.
Procedure
Belt Frictional Characteristics
1. Set the motor supply voltage to 12V and the angle of contact between the belt and pulley to 90°. Ensure
that the pulley direction is such that the weight tension is greater than the tension measured by the load
cell.
2. Vary the load T2 by hanging a range of weights on the belt. For each weight measure the string tension
T1 using the spring balance. Increase the loads until the motor nearly stalls. Do not leave the motor in its
stall condition for long periods since it will overheat.
3. Repeat the above procedure for belt/pulley contact angles of 180°, 270° and 360°.
DC Motor Efficiency
4. For one contact angle only, in addition to measuring the tensions, measure the motor voltage, current and
the pulley speed.
Results
1. Plot a graph of the tension T2 against T1 for each angle of contact. Bear in mind that T2 is always greater
than T1. The four curves should be plotted on the same graph. Estimate the best straight line fit to each
of the sets of results. Estimate the gradients of these lines (T2/T1) which will be used in part 2 below. This
is called the ‘belt tension ratio’.
2. Plot a graph of ln{Gradient (T2/T1)} against belt contact angle . Draw a best fit straight line through the
results and estimate the gradient. The coefficient of friction between the belt and pulley is given by the
gradient of this line.
3. Using the estimated coefficient of friction draw a graph of the theoretical belt tension ratio T2/T1 against
contact angle (not straight line). Plot the experimental belt tension ratio points on the same graph.
4. For the one angle of contact tested, calculate the motor input power, the motor output power and the
motor efficiency. Plot a graph of motor efficiency against torque.
Discussion
1. Are the results as expected? If not, why not.
2. Do the theoretical and experimental results agree?
3. Comment on the motor efficiency and explain the shape of the curve.
References
1. Grosjean, J., 'Principles of Dynamics', Stanley Thorne (Publishers) Ltd, ISBN 0 85950 295 3,1986.
2. Fawcett, J.N. and Burdess, J.S, 'Basic Mechanics With Engineering Applications', Edward Arnold, ISBN
0 7131 3620 0, 1988.
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